Monday, February 23, 2009

Distribution Systems I

In this paper Lee and Deininger explore the application of integer programming to optimize monitoring stations in simulated and real world water distribution systems. Under the requirements of the Clean Water Act water distribution systems are required to monitor the quality of water within the distribution system to ensure adequate quality. Although the law specifies the standards for drinking water distribution there are no explicit regulations regarding how to establish a compliant network for monitoring water quality within the system. To begin filling this gap Lee and Deininger apply linear programming to two hypothetical distribution systems as a proof of concept experiment before applying the process to two real world distribution networks.

Lee and Deininger began with a simple case using a hypothetical distribution network composed of seven interconnected nodes with known demands at each node. The nodes were linked by eight pipes with known flows between each node. The integer program was based on two assumptions:

1) the quality of water at any given node is representative of the quality at each upstream node and,

2) the quality varies as a function of the flow through each path leading to the node.

Using these two assumptions as the basis for determining the “coverage” at any node allowed Lee and Deininger to design a knowledge matrix the related the degree of network coverage provided by each node. The knowledge matrix was then used in the integer program to determine the optimal location of monitoring stations for network. They then expanded the process from the simple test network and applied it to the distribution network for Flint. Michigan. In doing so they were able to increase the coverage of the distribution network from its current value of ~18% to 54% without increasing the number of monitoring stations. Lee and Deininger followed this step by applying the same process to a hypothetical and real world distribution network that included daily shifts in the demands and flow patterns.

Overall this paper establishes the utility of integer programming for optimizing the location of monitoring stations within water distribution systems. By evolving the process from a simple proof of concept to a simple real world system and then on to more complex hypothetical and real world systems Lee and Deininger demonstrated the robust nature of their process. Unfortunately they neglected to include measures such as water use (domestic v. industrial) and population density associated with each node and instead based their model solely on flow and demand measurements. Including usage and population density would most likely have resulted in a different allocation of the monitoring stations.